We determine the interface free energy F(o.d.) between disordered and ordered phases in the q = 10 and q = 20 2d Potts models using the results of multicanonical Monte Carlo simulations on L2 lattices, and suitable finite-volume estimators. Our results, when extrapolated to the infinite-volume limit, agree to high precision with recent analytical calculations. At the transition point beta(t) the probability distribution function of the energy exhibits two maxima. Their locations have 1/L2 corrections, in contradiction with claims of 1/L behavior made in the literature. Our data show a flat region in between the two maxima which characterizes two domain configurations.